First of all, what are cumulative offset probability distribution (COPD) functions, and how are they used in earthquake offset analyses? In general, when scientists are trying to determine the size of past earthquakes, they need to know how much slip occurred in a single earthquake. This is because the magnitude of total offset is correlated to the moment magnitude/energy released during an earthquake (e.g., the Richter Scale). To determine the amount of total offset that occurs during earthquakes, we must find linear features that intersect the surface trace of a fault, and reconstruct the feature by ‘backslipping’ or undoing the motion that deformed that originally-linear feature. There are fantastic historic examples of roads and fences being split apart by earthquakes, but we may also use naturally sub-linear geologic features such as glacier moraines, streams, and ridges.
In Figure 1, a single point bar is right-laterally offset by a single fault trace.